All amplifiers will have some non-linearity across their dynamic range. Although there are contexts in which the resulting distortion in the amplified signal is desirable (such as an electric guitar amplifier), most applications do not benefit from non-linear distortion. For example, modern wireless telecommunication protocols such as 2.5G and 3G use non-constant amplitude (envelope modulation) signals. These non-constant envelope signals are sensitive to non-linear-power-amplifier-induced distortion. Given the general desire for linear power amplification, a number of techniques have been developed to enhance the linearity of power amplifiers. For example, feedforward power amplifiers have good linearity but generally do not improve efficiency and greatly increase cost and complexity.
An attractive alternative to feedforward linearization techniques is to pre-distort the input signal in an inverse fashion with regard to the non-linearity of the power amplifier. This pre-distortion may be performed on the input signal in the digital domain prior to a digital-to-analog conversion. Alternatively, the input signal may be pre-distorted in the analog RF domain. To pre-distort the input signal in the RF domain, the input signal is typically multiplied with the pre-distortion signal. For example, an RF input signal that will be multiplied by the pre-distortion signal may be represented by the real part of {R(t)*exp(jωct)}, where R(t) is the complex envelope, j is the imaginary unit, ωc is the angular frequency of the RF carrier bearing the complex envelop modulation, and t is time. The desired pre-distortion of the complex envelope may be better understood with reference to FIG. 1, which illustrates the non-linear dependence of an output signal amplitude 101 with respect to input signal amplitude for a conventional amplifier. As known in the arts, a conventional amplifier has a linear region of operation and a saturation region of operation (these regions being separated by dashed line 106 in FIG. 1). For relatively small input signal amplitudes, a real-world amplifier will amplify such small signal amplitudes into corresponding output signal amplitudes according to the gain of the amplifier in a close-to-perfectly-linear fashion. However, as the amplifier approaches saturation, output signal amplitude 101 progressively distorts away from an ideal linear response for the amplifier (the ideal linear response for a perfect amplifier being represented by dashed line 100). Given this non-linearity, it may be seen that if the input signal amplitudes to the amplifier were pre-distorted in a reciprocal fashion to the distortion seen in output signal amplitude 101 with respect to ideal response 100, the amplifier would provide an output signal that would mirror ideal response 100. As seen by an output signal amplitude 105 (which would be produced by an ideal amplifier amplifying the pre-distorted signal), the pre-distortion mirrors the distortion in output signal amplitude 101 with respect to ideal response 100. By multiplying such a pre-distortion signal with the input signal, the amplifier is thereby linearized, to the limit of saturation for the amplifier in question.
Referring back to the complex envelope representation of the RF input signal, it may be seen that the pre-distortion signal is a baseband signal in that the pre-distortion signal is a function of the complex envelope R(t) and not of the RF carrier. In that regard, a pre-distortion signal that will be multiplied by the complex envelope may be represented as a Taylor series expression: α1+α2*R(t)+α3*R(t)2+α4*R(t)3+ . . . , where the alpha symbols represent complex series coefficients. Upon multiplication with the RF input signal (the real part of {R(t)*exp(jωct)}), the resulting pre-distorted RF signal becomes the real part of {[α1*R(t)+α2*R(t)2+α3*R(t)3+α4*R(t)4+ . . . ]*exp(j ωct)} that will then form an input signal for the amplifier. The alpha coefficients are controlled so as to pre-distort the input signal so as to produce a linear response in the downstream amplifier.
Turning now to FIG. 2, an RF signal processing (RFSP) circuit 200 that addresses the non-linear distortion discussed with regard to FIG. 1 is illustrated. An amplifier 205 amplifies an RF input signal 201 (designated as the complex signal (R(t)exp(jωct)) after it has been properly pre-distorted such that a resulting output signal 210 from the amplifier is amplified in a substantially linear fashion. To generate an appropriate pre distortion pre-distorted signal 265, the degree of non-linearity in this output signal should be determined so that the degree of pre-distortion necessary to linearize amplifier 205 may in turn be determined. The non-linearity of amplifier 205 may be determined in a number of fashions. For example, a version of output RF signal 210 may be suitably scaled in an attenuator 215 and have its sign reversed through a 180 degree phase-shifter 220 so that it may be subtracted from a version of the RF input signal in an adder 225 to produce an error signal e(t) 226. Each version of the RF input signal and the RF output signal is supplied through, for example, couplers 230. Based upon the non-linearity as exhibited in error signal 226, a signal generator 235 may then generate an appropriate pre-distortion signal 236 such as the complex Taylor series discussed above: α1+α2*R(t)+α3*R(t)2+α4*R(t)3 and so on up until some final power of R(t). This final power depends upon the complexity of the design and desired precision. For example, suppose the final power in the series expression is five, corresponding to R(t)5. In such an embodiment, it may be seen that signal generator must then solve for six coefficients in the Taylor series, ranging from α1 to α6. The envelope function associated with each coefficient may be designated as the corresponding “basis” function. Thus the monomial basis function associated with coefficient α1 is R(t)0, the basis function associated with coefficient α2 is R(t)1, the basis function associated with coefficient α3 is R(t)2, and so on. These coefficients may be determined in a variety of fashions. In an example analytical approach, signal generator 235 may include a correlator for each coefficient. Each coefficient's correlator correlates error signal 226 with the basis function corresponding to the coefficient. For example, coefficient α2 may be produced responsive to a correlation of the error signal and the envelope R(t), coefficient α3 may be produced responsive to a correlation of the error signal and the squared envelope R(t)2, and so on. It may be shown that the preceding selection of monomial basis functions will not typically provide desirable real-world results because numerous calculation cycles are necessary to converge to a solution. To enhance the convergence speed, each basis function may be an orthonormal polynomial formed from the above-discussed monomial powers of R(t) such as discussed in U.S. application Ser. No. 11/484,008, filed Jul. 7, 2006, now U.S. Pat. No. 7,844,014, the contents of which are incorporated by reference. The correlation of the basis functions and the error functions may be performed in an analog domain or in a digital domain. In alternative embodiments, signal generator 235 may simply use a brute force approach or non-linear optimization techniques to select an appropriate value for the coefficients such that the error signal is minimized.
Regardless of how signal generator 235 processes the error signal, signal generator 235 will determine values for the coefficients in the series representation of pre-distorted RF input signal 265 as discussed above. The number of coefficients depends upon the highest power of the complex envelope R(t) that will be generated for pre-distorted RF input signal 265. For example, signal generator 235 may generate up to a sixth power of the complex envelope R(t) in a complex pre-distortion signal 236 represented as (α1+α2*R(t)1+α3*R(t)2+α4(t)3+α5*R(t)4+α6*R(t)5+α7*R(t)6). Depending upon the resulting non-linearity produced in output RF signal 210 for a given set of coefficients, the signal generator may then drive the coefficients (from α1 to α7) until the non-linearity reaches a minimal value.
In this fashion, signal generator 235 functions to cancel the non-linear components in RF output signal 210. For example, suppose the amplifier has a non-linearity such that it produces a component proportional to R(t)2 having a certain phase relationship to the baseband envelope R(t). Signal generator 235 must then generate the coefficients such that this R(t)2 component is cancelled in the RF output signal. It may thus be seen that each coefficient may require a unique and independent phase relationship to the baseband signal so that the corresponding non-linear component in the RF output signal may be cancelled. To enable such independent phasing, the multiplication of RF input signal 201 and pre-distortion signal 236 should be performed in the in-phase (I) and quadrature (Q) domain. Thus, the RF input signal R(t) may be decomposed into its I and Q components after passing through a buffer 240 and a quadrature phase-shifter (QPS) 245. Signal generator 235 generates its coefficients in corresponding I and Q forms (designated in FIG. 2 as the real (Re) and imaginary (Im) parts of pre-distortion signal 236, respectively). The resulting I components of the RF input signal and the pre-distortion signal are multiplied in a mixer 250. Similarly, the resulting Q components of the RF input signal and the pre-distortion signal are multiplied in a mixer 255. The mixer output signals may be combined in a combiner 260 to provide pre-distorted RF input signal 265 to the amplifier.
But note that the generation of the analog non-linear components R(t)2, R(t)3, etc., in the signal generator is an inherently noisy process. The noise in the pre-distortion signal may then dominate the resulting pre-distorted RF input signal 265 that is to be amplified as shown by the following analysis: Let the input signal to be pre-distorted be represented by X such that its signal-power-to-noise-power ratio (SNRX) is X2/(nx)2, where nx represents the rms noise “n” in the input signal X. Similarly, the pre-distortion signal may be represented by Y such that its signal-power-to-noise-power ratio (SNRY) is Y2/(ny)2. The multiplied signal (corresponding to pre-distorted RF input signal 265) is thus represented by Y*X. It may then be shown that the SNR for the signal YX is 1/((1/SNRX)+(1/SNRY)). This expression for output SNR indicates that the output SNR is lower than the lowest SNR of the two inputs. This is a worst case scenario for the output SNR because the pre-distortion signal Y is typically noisy as compared to the input signal X. For example, suppose SNRX is 100,000 and SNRY is 10,000 such that the RF input signal X is 10 times less noisy than the pre-distortion signal Y. However, the output SNR will be 9,091, slightly less than the pre-distortion signal's SNRY because of its SNR dependence discussed above.
Because pre-distortion in the RF domain is noisy, linearization using pre-distortion is typically performed in the digital domain. However, digital pre-distortion has its own problems because of the sampling noise introduced by the required conversions of the pre-distortion signal into the digital domain and then back into the analog domain. Moreover, these conversions use large amounts of power (often as much as a low-power power amplifier) and require complex circuitry. Accordingly, there is a need in the art for more robust pre-distortion techniques.